Some automatic design techniques for analog circuits take into consideration the yield. In such automatic design techniques, when plural sample points are generated, each of which has plural kinds of performance item values (these are also called performances, totally. For example, gain, power consumption, linearity, area, noise, accuracy, dynamic range, impedance matching or the like) that are simulation results for combinations of specific design parameters and specific design variable values, while changing values in the combinations, the yield as represented below is defined for each of plural sample points.
On the premise, “the performance P1 at the sample point 1 dominates the performance P2 at the sample point 2” is defined as follows:P1P2∀i(p1i≦p2i)∃i(p1i≦p2i),i=1 . . . N  (1)
p1i represents a value of the i-th performance item included in the performance P1, and p2i represents a value of the i-th performance item included in the performance P2. The expression (1) represents that, when values of all of the performance items at the sample point 1 are equivalent to or better than values of the corresponding performance items at the sample point 2, and a value of any one performance item at the sample point 1 is better than a value of a corresponding performance item at the sample point 2, it is said that the performance P1 dominates the performance P2. When the performance P1 dominates the performance P2, it is also said that the sample point 1 dominates the sample point 2.
In addition, the domination relationship of the performance will be explained by using FIG. 1. Here, it is assumed that there are only two performance items, and the first performance item is represented by the vertical axis as a performance item 1, and the performance is higher when the lesser value is obtained. Moreover, it is assumed that the second performance item is represented by the horizontal axis as a performance item 2, and when the lesser value is obtained, the performance is higher. Here, when values of the performance items 1 and 2 are identified by carrying out the simulation, sample points are plotted on 2-dimensional space as illustrated in FIG. 1. In an example of FIG. 1, 6 sample points A to F are obtained. In such a situation, because the lesser value is naturally preferable for any of the performance items 1 and 2, the sample point which is nearer to the origin is better.
Then, “X dominates Y” represents that all components (i.e. performance item value) of Y is equal to or worse than the corresponding components of X, and at least one of the components of Y is worse than the corresponding component of X. In the two-dimensional space as illustrated in FIG. 1, because B whose values of the performance items 1 and 2 are lesser is a better sampling point than E, “B dominates E”, and similarly, because C is a better sampling point than F, “C dominates F”. On the other hand, when A is compared with B, because the A's value of the performance item 2 is lesser but the B's value of the performance item 1 is lesser, it cannot be said that “A dominates B”. As for A to D, the dominancy relationship is not satisfied. Thus, the sampling points that are not dominated by the other sampling point in the performance space are called “Pareto” (also called “non-dominant solution”). Then, a curve A (in case of the three-dimensional or higher dimensional space, curved surface) connecting the Pareto is called “Pareto curve” (or “Pareto curved surface”).
In addition, as illustrated in FIG. 2, the sample point is plotted at a position of a circle mark according to the performance item values, and a sample point focused this time is illustrated by a black circle. Incidentally, an ellipse with a hatch virtually represents a distribution area of the sample points. In such a case, sample points having the equivalent to or better values than those of the focused sample point for all of the performance items are sample points included in a rectangle measurement range whose upper right vertex is the black circle. Incidentally, the condition is similar even when the number of performance items is three or more.
In the aforementioned conventional technique, the appearance probability of the sample points having the performance equivalent to or better than that of a focused sample point is defined as the yield. Therefore, the yield is calculated by counting (the number of sample points that appear in the measurement range illustrated in FIG. 2 +1) and dividing the counted value by the number of all sample points.
However, when the yields are calculated for all sample points, a processing to confirm, for each focused sample point, the domination relationship with the other sample points is carried out. Accordingly, when the number of samples increases, it takes an extremely long processing time.
Namely, there is no technique for rapidly calculating the yield based on the domination relationship between sample points.